Question

1. what is the rule for reflections over the x - axis? (x + h,y + k) (x,y) (-x,y) (y,x) (y,-x) 4) what is the rule for translations on the graph? (x + h,y + k) (x,y) (-x,y) (y,x) (y,-x) questions 5 - 6

Explanation:

1. For the rule of reflection over the x - axis:

• # Explanation:
• ## Step1: Recall reflection concept
• When reflecting a point \((x,y)\) over the x - axis, the x - coordinate remains the same and the y - coordinate changes its sign.
• The general rule for reflecting a point \((x,y)\) over the x - axis is \((x, - y)\). But among the given options, it seems there are some typos. If we assume the correct form of the rule is among the options, we know the correct transformation.
• # Answer:
• None of the given options are correct. The correct rule for reflection over the x - axis is \((x,-y)\).

1. For the rule of translations on the graph:

• # Explanation:
• ## Step1: Recall translation concept
• In a translation of a point \((x,y)\) on a graph, we move the point horizontally by \(h\) units and vertically by \(k\) units.
• The rule for translating a point \((x,y)\) is \((x + h,y + k)\), where \(h\) is the horizontal displacement and \(k\) is the vertical displacement. If \(h>0\), we move right, if \(h < 0\) we move left, if \(k>0\) we move up and if \(k < 0\) we move down.
• # Answer:
• \((x + h,y + k)\)

Answer:

1. For the rule of reflection over the x - axis:

• # Explanation:
• ## Step1: Recall reflection concept
• When reflecting a point \((x,y)\) over the x - axis, the x - coordinate remains the same and the y - coordinate changes its sign.
• The general rule for reflecting a point \((x,y)\) over the x - axis is \((x, - y)\). But among the given options, it seems there are some typos. If we assume the correct form of the rule is among the options, we know the correct transformation.
• # Answer:
• None of the given options are correct. The correct rule for reflection over the x - axis is \((x,-y)\).

1. For the rule of translations on the graph:

• # Explanation:
• ## Step1: Recall translation concept
• In a translation of a point \((x,y)\) on a graph, we move the point horizontally by \(h\) units and vertically by \(k\) units.
• The rule for translating a point \((x,y)\) is \((x + h,y + k)\), where \(h\) is the horizontal displacement and \(k\) is the vertical displacement. If \(h>0\), we move right, if \(h < 0\) we move left, if \(k>0\) we move up and if \(k < 0\) we move down.
• # Answer:
• \((x + h,y + k)\)